{
  "id": "1505.04386",
  "version": "v1",
  "published": "2015-05-17T12:12:45.000Z",
  "updated": "2015-05-17T12:12:45.000Z",
  "title": "Annular Khovanov homology and knotted Schur-Weyl representations",
  "authors": [
    "J. Elisenda Grigsby",
    "Anthony M. Licata",
    "Stephan M. Wehrli"
  ],
  "comment": "38 pages, 8 figures",
  "categories": [
    "math.GT",
    "math.QA",
    "math.RT"
  ],
  "abstract": "Let L be a link in a thickened annulus. We show that its sutured annular Khovanov homology carries an action of the exterior current algebra of the Lie algebra sl_2. When L is an m-framed n-cable of a knot K in the three-sphere, its sutured annular Khovanov homology carries a commuting action of the symmetric group S_n. One therefore obtains a \"knotted\" Schur-Weyl representation that agrees with classical sl_2 Schur-Weyl duality when K is the Seifert-framed unknot.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-17T12:12:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27",
      "81R50",
      "20F36"
    ],
    "keywords": [
      "knotted schur-weyl representations",
      "sutured annular khovanov homology carries",
      "exterior current algebra",
      "schur-weyl duality",
      "lie algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150504386E"
    }
  }
}